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Simplifying x2 + 3x + -60 + 17x + -30 = 90 Reorder the terms: -60 + -30 + 3x + 17x + x2 = 90 Combine like terms: -60 + -30 = -90 -90 + 3x + 17x + x2 = 90 Combine like terms: 3x + 17x = 20x -90 + 20x + x2 = 90 Solving -90 + 20x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -90 + 20x + x2 = 90 + -90 Combine like terms: -90 + -90 = -180 -180 + 20x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -180 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 20x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 20x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 20x + x2 = 0 + 180 20x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 20x + x2 = 180 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 180 + 100 Reorder the terms: 100 + 20x + x2 = 180 + 100 Combine like terms: 180 + 100 = 280 100 + 20x + x2 = 280 Factor a perfect square on the left side: (x + 10)(x + 10) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + 10) equal to 16.733200531 and -16.733200531.Subproblem 1
x + 10 = 16.733200531 Simplifying x + 10 = 16.733200531 Reorder the terms: 10 + x = 16.733200531 Solving 10 + x = 16.733200531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 16.733200531 + -10 Combine like terms: 10 + -10 = 0 0 + x = 16.733200531 + -10 x = 16.733200531 + -10 Combine like terms: 16.733200531 + -10 = 6.733200531 x = 6.733200531 Simplifying x = 6.733200531Subproblem 2
x + 10 = -16.733200531 Simplifying x + 10 = -16.733200531 Reorder the terms: 10 + x = -16.733200531 Solving 10 + x = -16.733200531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -16.733200531 + -10 Combine like terms: 10 + -10 = 0 0 + x = -16.733200531 + -10 x = -16.733200531 + -10 Combine like terms: -16.733200531 + -10 = -26.733200531 x = -26.733200531 Simplifying x = -26.733200531Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.733200531, -26.733200531}
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